The in-plane resistivity anisotropy has been measured for detwinned single crystals of Ba(Fe 1-xNi x)₂As₂ and Ba(Fe 1-xCu x)₂As₂. The data reveal a nonmonotonic doping dependence, similar to previous observations for Ba(Fe 1-xCo x)₂As₂. Magnetotransport measurements of the parent compound reveal a nonlinear Hall coefficient and a large linear term in the transverse magnetoresistance. Both effects are rapidly suppressed with chemical substitution over a similar compositional range as the onset of the large in-plane resistivity anisotropy. This suggests that the relatively small in-plane anisotropy of the parent compound in the spin-density wave state is due to the presence of anmore » isotropic, high mobility pocket of the reconstructed Fermi surface. Progressive suppression of the contribution to the conductivity arising from this isotropic pocket with chemical substitution eventually reveals the underlying in-plane anisotropy associated with the remaining Fermi surface pockets« less